How can I make a material that is transparent at the center and emission at the corners of a plane
Some function of (distance from object origin) will give you a circle to do what you want with.. here, using a Map Range to soften the mask, which is plugged into the alpha-channel of an emissive material. If you need to have the center of the circle somewhere else, you could use another object's origin, using the option near the bottom of the Texture Coordinate node.